\documentclass{amsart}

\usepackage{amsmath}


\usepackage{mathtools}
\usepackage{ocgx}

\newsavebox{\tempbox}% simplify source
\newsavebox{\switchbox}% measure width
\savebox{\switchbox}{\fcolorbox{blue}{red}{\bfseries +}}

\newcommand{\centerwithin}[2]{% #1=small symbol, #2=wide symbol
    {\mathmakebox[\widthof{\ensuremath{{}#2{}}}][c]{{#1}}}}


\begin{document}

\begin{align*}
\bigwedge_{i=1}^{2} &\centerwithin\bigwedge_{n=1}^{2} \bigvee_{j=1}^{2}~p(i,j,n)=\\
=\left(\bigwedge_{n=1}^{2} \bigvee_{j=1}^{2}\ p(1,j,n)\right) &\wedge \left(\bigwedge_{n=1}^{2} \bigvee_{j=1}^{2}\ p(2,j,n)\right)=\\
=\left(\bigvee_{j=1}^{2}\ p(1,j,1)\wedge \bigvee_{j=1}^{2}\ p(1,j,2)\right) &\wedge \left( \bigvee_{j=1}^{2}\ p(2,j,1)\wedge \bigvee_{j=1}^{2}\ p(2,j,2)\right)=\\
=(p(1,1,1)\vee p(1,2,1))\wedge (p(1,1,2)\vee  p(1,2,2)) &\wedge (p(2,1,1)\vee p(2,2,1))\wedge (p(2,1,2)\vee p(2,2,2))
\end{align*}


\end{document}